Bike further
Min
2025-04-10
Describ the data
Number of nodes: 542
Number of total events: 3542684
Time spends: 2018-04 to 2018-12
The density of a bike station is measured in terms of the number of neighboring stations. We denote by \(n(i)\) the average of:
- the number of bike stations which can be reached from \(i\) in less than three minutes and
- the number of bike stations from which \(i\) can be reached in less than three minutes.
The feature vector is defined as: \[ X_{n,ij} := \begin{pmatrix} \log(d_{i,j} \vee 1) \\ \log(d_{i,j} \vee 1)^2 \\ \log(n(i) \vee 1) \\ \log(n(j) \vee 1) \end{pmatrix} \]
1. The gamma estimator plots (compare with k’th methods)
2. The \(\alpha_i\) and \(\beta_i\) for all individuals
2.1 Overall \(\alpha_i\) and \(\beta_i\).
#### Top 6 individuals with the highest cumulative indegree/outdegree
Top 6 individuals with the highest volatility in indegree/outdegree
2.2 Four stations as example:
We use bike stations 101, 301, 401, 501 as an example, where 301/501 show the same trends and 101/401 show the same trends.
## id Start.station start_long start_lat
## 1 101 20th St & Virginia Ave NW -77.04513 38.89472
## 2 301 Georgia Ave and Fairmont St NW -77.02261 38.92482
## 3 401 New Hampshire Ave & T St NW -77.03825 38.91554
## 4 501 Tysons West Transit Center -77.23177 38.93270301 alpha
501 alpha
301 beta
501 beta
101 alpha
401 alpha
101 beta
401 beta
Our model reveals distinct activity patterns across bike-sharing stations during public holidays (05-25, 09-06, and 11-11). Stations in central Washington, D.C.—20th St & Virginia Ave NW and New Hampshire Ave & T St NW—exhibit a marked decline in activity, while those in Northwest D.C. (Georgia Ave and Fairmont St NW) and Tysons, Virginia (Tysons West Transit Center) show significant increases. This divergence likely stems from the interplay of geographical location and holiday-driven behavior. In the urban core, residents’ outbound travel and reduced commercial activity during holidays like Memorial Day, Labor Day, and Veterans Day decrease bike usage. Conversely, the Northwest D.C. station, near Howard University, benefits from students and locals engaging in recreational cycling during these breaks. Meanwhile, Tysons West Transit Center, a transit hub, sees heightened activity as holiday travelers arrive via public transport and use bikes for short trips or leisure, supported by its proximity to commercial and recreational amenities. These findings highlight how location-specific activity patterns and holiday timing shape bike-sharing dynamics
3. Clusters
- Cluster the stations, by the estimated \(\alpha_i(t)\) and \(\beta_i(t)\).
3.1 Cluster by perdetermined features
Features: - mean indegree: \(\int \alpha_i(t)dt\) - mean outdegree: \(\int \alpha_i(t)dt\) - sd indegree: \(\int (\alpha_i(t) - \bar \alpha(t))^2 dt\) - sd outdegree: \(\int (\beta_i(t) - \bar \beta(t))^2 dt\) - slope indegree: \(\alpha_i(t) \sim \theta_i*t\) - slope outdegree: \(\beta_i(t) \sim \theta_i*t\) - peak time: \(\max_{t} (\alpha_i(t)-\beta_i(t))\)
Clustering was conducted by Kmeans algorithm.
3.2 Cluster: by all xxx_a, xxx_b
Combine \(\alpha_i(t)\) and \(\beta_i(t)\) and apply the Kmeans algorithm.
4. Group Changes
To evalue the time volatility of \(\alpha\) and \(\beta\)
We first Divide the observation period into 9 intervals by months (from Apr to Dec): \(T_1,...T_9\).
For \(t\)th interval, categorize individuals into 4 groups based on \(\int_{T_t} \alpha(t)dt\): indegree and \(\int_{T_t} \beta(t) dt\): The thresholds was obtained by the overall median: \(\text{median }_{i=1,...,n,t=1,...,T } \alpha_i(t)\) and \(\text{median }_{i=1,...,n,t=1,...,T } \beta_i(t)\).
- High In & High Out
- High In & Low Out
- Low In & High Out
- Low In & Low Out
Compute the proportion of individuals shifting between categories across intervals. Use alluvial diagrams to illustrate the transitions
4.1 Flow Plots
The alluvial diagrams reveal two distinct transport patterns in the bike-sharing network:
Persistent Asymmetry Deficit The proportion of stations exhibiting transport asymmetry (High-In/Low-Out \(\le 5\%\); Low-In/High-Out \(\le 6\%\)) remains consistently low throughout observed cycles. This contrasts sharply with social network reciprocity where nodes typically show follower/following asymmetry (High-In/Low-Out \(\le 41\%\); Low-In/High-Out \(\le 30\%\)), indicating fundamental differences in directional flow mechanisms between social and transport networks. This indicates The proposed model effectively captures the dynamic characteristics of bike-sharing stations, reflecting real-world operational features.
Seasonal Demand Polarization Furthermore, the model identifies seasonal demand polarization, where ‘High In/High Out’ stations exhibit cyclical behavior: demand peaks in April, gradually declines in summer, and rebounds in autumn, aligning with external factors such as weather and urban activity patterns. These findings demonstrate that the model is robust in characterizing the structural stability and temporal adaptability of the bike-sharing network, providing a valuable framework for optimizing resource allocation and station management.
4.2 Trans propotions Plots
